shannon wavelets - t is a scaling function, what about the...

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SHANNON WAVELET Its Fourier transform, given by is bandlimited to the frequency range   . It also satisfies the Poisson summation formula equation (1), indicating that ( ) H and its integer translates are orthogonal. In fact, ( ) t satisfies the orthonormality condition. If it were also to satisfy the two-scale relation, it would qualify as a scaling function. Let us verify that it does by substituting Equation (2) into Equation (3) and then transforming it into the frequency domain. We are looking for a filter H with an impulse response h(n) such that Taking Fourier transform on both sides ( ) H which satisfies the above equation is which is an ideal LPF with cutoff frequency / 2 . It can be verified that ( ) H satisfies the PRQMF property. we know that ( )
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Unformatted text preview: t is a scaling function, what about the corresponding wavelet? We again operate in the frequency domain to find the wavelet. By taking the Fourier transform to both sides of below equation we get equation (4), we have its frequency domain equivalent. For our ideal ( ) H Create PDF files without this message by purchasing novaPDF printer ( http://www.novapdf.com ) Which is an ideal HPF. Because of the association of the sinc function with sampling theory, the scaling function ( ) t is known as the Shannon scaling function, and the wavelet is known as the Shannon wavelet which is bandlimited. Create PDF files without this message by purchasing novaPDF printer ( http://www.novapdf.com )...
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shannon wavelets - t is a scaling function, what about the...

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